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Exact solution of a triaxial gyrostat with one rotor

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Abstract

The problem of the attitude dynamics of a triaxial gyrostat under no external torques and one constant internal rotor, is a three degrees-of-freedom system, although thanks to the existence of integrals of motion it can be reduced to only one degree-of-freedom problem. We introduce coordinates to represent the orbits of constant angular momentum as a flow on a sphere. This representation shows that the problem is equivalent to a quadratic Hamiltonian depending on two parameters. We find the exact solution of the orbits in terms of elliptic functions. By making use of properties of elliptic functions we find the solution at each region of the parametric partition from the solution of one region. We also prove that heteroclinic orbits are planar curves.

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Authors and Affiliations

  1. Grupo de Mecánica Espacial and IUMA, Universidad de Zaragoza, 50009, Zaragoza, Spain

    Antonio Elipe

  2. Department of Mathematics and Computation, Universidad de la Rioja, 26004, Logroño, Spain

    Víctor Lanchares

Authors
  1. Antonio Elipe
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  2. Víctor Lanchares
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Correspondence to Antonio Elipe.

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Elipe, A., Lanchares, V. Exact solution of a triaxial gyrostat with one rotor. Celest Mech Dyn Astr 101, 49–68 (2008). https://doi.org/10.1007/s10569-008-9129-6

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  • DOI: https://doi.org/10.1007/s10569-008-9129-6

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